共查询到19条相似文献,搜索用时 125 毫秒
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具有功能性反应函数xn/n+1的捕食系统 总被引:10,自引:3,他引:7
讨论了具有功能性反应函数为x^n/n 1的捕食系统,其中n是任意正整数.证明了此系统如存在正平衡点必唯一,且必全局生态稳定.并讨论了此唯一正平衡点的Hopf分支. 相似文献
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捕食者有病的生态-流行病模型的分析 总被引:11,自引:1,他引:10
建立并分析了捕食者具有疾病且有功能反应的生态-流行病(SI)模型,讨论了解的有界性.应用特征根法得到了平衡点局部渐近稳定的充分条件,进一步分析了平衡点的全局稳定性,得到了边界平衡点和正平衡点全局稳定的充分条件。 相似文献
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本文运用常微分方程稳定性理论及方法讨论了一类具有相互干扰的捕食与被捕食模型的稳定性,得到了正平衡点的局部稳定性条件,正平衡点在第一象限的全局稳定性条件及解的有界性. 相似文献
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本文讨论了三种竞争种群的古典GLV系统.对系统所有非负平衡点的稳定性,进行了分析,给出了正平衡点全局稳定的充分条件,应用Hopf分支定理,我们给出了系统具有分支值的充分条件. 相似文献
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本文讨论了一类具有强连续时滞的捕食-被捕食模型,分析了各非负平衡点的稳定性,利用区域连续收缩方法,得出非负平衡点全局稳定的充分条件,给出正平衡点全局稳定的充分条件,并给出系统出现Hopf的分支值. 相似文献
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一类具Holling Ⅲ型功能反应的捕食者-食饵模型的定性分析 总被引:4,自引:0,他引:4
研究一类具Holling Ⅲ型功能反应的捕食者一食饵模型.应用定性分析和Hopf分支理论,得到了一个正平衡点的全局稳定性、三个正平衡点的局部稳定性和极限环的存在性的充分条件,使用MATLAB软件。本文给出了三个例子来模拟这些结论。 相似文献
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具非线性饱和功能反应的捕食者-食饵系统的定性分析 总被引:1,自引:0,他引:1
研究了一类具有非线性饱和功能反应的捕食者—食饵系统的定性行为.结果表明:当正平衡点稳定时,系统为全局渐近稳定的;当正平衡点不稳定时,系统存在唯一稳定的极限环. 相似文献
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This paper presents a resource-dependent viability selection differential equation model of continuously reproducing diploid population with two alleles at one locus for a single limiting resource. This model assumes that the genotypic fitness is only a function of the limiting resource. The conditions that the interior equilibrium point of the system exists are that the heterozygote fitness is positive and the homozygote fitness is negative, or the heterozygote fitness is negative and the homozygote fitness is positive at the point. The sufficient and necessary conditions of locally asymptotical stability of the interior equilibrium point are that the heterozygote fitness is positive at the point, or the locally asymptotically stable equilibrium corresponds to the point at which the level of the limiting resource is locally minimized on the zero mean fitness curve, f = 0. 相似文献
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In this paper, we propose a prey–predator system with stage structure for predator. The proposed system incorporates cannibalism for predator populations in a competitive environment. The combined fishing effort is considered as control used to harvest the populations. The steady states of the system are determined and the dynamical behavior of the system is discussed. Local stability of the system is analyzed and sufficient conditions are derived for the global stability of the system at the positive equilibrium point. The existence of the Hopf bifurcation phenomenon is examined at the positive equilibrium point of the proposed system. We consider harvesting effort as a control parameter and subsequently, characterize the optimal control parameter in order to formulate the optimal control problem under the dynamic framework towards optimal utilization of the resource. Moreover, the optimal system is solved numerically to investigate the sustainability of the ecosystem using an iterative method with a Runge–Kutta fourth-order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. Results are analyzed with the help of graphical illustrations. 相似文献
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In this paper, we consider permanence of Lotka-Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka-Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence. 相似文献
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一个稀疏效应下的Volterra系统的极限环 总被引:16,自引:0,他引:16
应用数学生态学和微分方程定性理论,讨论了一个稀疏效应下的Volterra系统,在给定参数满足一定的条件下,证明了该系统极限环的存在性和唯一性,以及该系统的正平衡点全局渐近稳定。 相似文献
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It takes time for individuals to move from place to place. This travel time can be incorporated into metapopulation models via a delay in the interpatch migration term. Such a term has been shown to stabilize the positive equilibrium of the classical Lotka-Volterra predator-prey system with one species (either the predator or the prey) dispersing. We study a more realistic, Rosenzweig-MacArthur, model that includes a carrying capacity for the prey, and saturating functional response for the predator. We show that dispersal delays can stabilize the predator-prey equilibrium point despite the presence of a Type II functional response that is known to be destabilizing. We also show that dispersal delays reduce the amplitude of oscillations when the equilibrium is unstable, and therefore may help resolve the paradox of enrichment. 相似文献